The Internet Is Like A Jellyfisheclectic.ss.uci.edu/~drwhite/center/ppt_pdf/LATEST-jellyfish.pdf ·...
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The Internet Is Like A JellyfishThe Internet Is Like A Jellyfish
Michalis FaloutsosMichalis FaloutsosUC RiversideUC Riverside
Joint work with:Joint work with:Leslie Leslie TauroTauro, , GeorgosGeorgos SiganosSiganos (UCR)(UCR)Chris Palmer(CMU) Chris Palmer(CMU)
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Big Picture: Modeling the InternetBig Picture: Modeling the Internet
Measure and model each componentMeasure and model each component•• Identify simple properties and patternsIdentify simple properties and patterns
Model and simulate their interactionsModel and simulate their interactions
Topology
Protocols
Traffic
Routing, Congestion ControlRouting, Congestion Control
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Power-law: Frequency of degree vs. degree
The Goal of Internet ModelingThe Goal of Internet Modeling
Find Find simplesimple fundamental propertiesfundamental propertiesUnderstand why they appear and their effectsUnderstand why they appear and their effects
A real Internet instance
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Claim: We Need The Right ToolsClaim: We Need The Right Tools
““This is just not effectiveThis is just not effective……
We need to get some chainsWe need to get some chains””The Far Side -- G. Larson
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The World Wide Web is a BowThe World Wide Web is a Bow--TieTie
Captures several properties [Captures several properties [WWWWWW--TomkinsTomkins et alet al]]The components are of comparable sizeThe components are of comparable size
In outStrongly connected
•Core•In•Out•Tendrils
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The AccuracyThe Accuracy--Intuition Space Of Intuition Space Of ModelsModels
More toolsMore tools……•• SelfSelf--similaritysimilarity•• PowerPower--lawslaws•• WaveletsWavelets•• EigenvaluesEigenvalues
……less intuitionless intuition•• Something a human Something a human
can picture can picture
Is it a real conflict?Is it a real conflict?Accuracy
IntuitionIdeal
Clueless
trend
low
low high
high Naive
Complex
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Why Do We Need an Intuitive Model?Why Do We Need an Intuitive Model?
Human mind is simpleHuman mind is simpleVisualizableVisualizable: creates a mental picture: creates a mental pictureMemorable: captures the main propertiesMemorable: captures the main propertiesMaximizesMaximizes information/effortinformation/effort ratioratioMakes you thinkMakes you think
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What does the Internet look like?What does the Internet look like?
Can I develop a simple model of the AS Can I develop a simple model of the AS Internet topology that I can Internet topology that I can draw by handdraw by hand??Can I identify a sense of hierarchy in the Can I identify a sense of hierarchy in the network?network?
Focus: Autonomous Systems topologyFocus: Autonomous Systems topologyand data from NLANRand data from NLANR
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Possible Topological ModelsPossible Topological Models
FurballFurball BroomBroom DonutDonut(One(One--degree nodes degree nodes
are at the are at the periphery)periphery)
(Military (Military Hierarchy)Hierarchy)
(Circular (Circular connectivity:connectivity:
Around the earth?)Around the earth?)
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An Intuitive Model : The Internet An Intuitive Model : The Internet Topology as JellyfishTopology as Jellyfish
Highly connected nodes Highly connected nodes form the coreform the coreEach Shell: adjacent Each Shell: adjacent nodes of previous shell, nodes of previous shell, except 1except 1--degree nodesdegree nodesImportanceImportance decreases as decreases as we move away from corewe move away from core11--degree nodes hangingdegree nodes hangingThe denser the 1The denser the 1--degree degree node population the node population the longer the stemlonger the stem
CoreShells 123
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Roadmap Roadmap
Identify a HierarchyIdentify a Hierarchy•• Define the Importance of a nodeDefine the Importance of a node
Present topological propertiesPresent topological propertiesPresent the jellyfish model Present the jellyfish model Why is the jellyfish a good model?Why is the jellyfish a good model?ConclusionsConclusionsAppendix: Latest News on powerAppendix: Latest News on power--laws for the laws for the Internet topologyInternet topology
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How Can We Develop a Simple How Can We Develop a Simple Model?Model?
We need an anchor and a compassWe need an anchor and a compassAnchor: Anchor: •• We need a starting point in the networkWe need a starting point in the network
Compass:Compass:•• We want to classify nodes according to We want to classify nodes according to importanceimportance
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Defining the Importance of a NodeDefining the Importance of a Node
The topological importance has many The topological importance has many aspectsaspectsDegreeDegree: number of adjacent nodes: number of adjacent nodesEccentricityEccentricity: the maximum distance: the maximum distanceto any other nodeto any other node
SignificanceSignificance: Significant nodes are near :: Significant nodes are near :1.1. many nodesmany nodes2.2. significant nodessignificant nodes
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Significance of a NodeSignificance of a Node
The significance of a node is the sum of the The significance of a node is the sum of the significance of its neighbors.significance of its neighbors.The iterative procedure convergesThe iterative procedure converges•• At each round, total significance is normalized to 1At each round, total significance is normalized to 1
This is equivalent to This is equivalent to [Kleinberg [Kleinberg ‘‘96]96]::•• the eigenvector of the max the eigenvector of the max eigenvalueeigenvalue of the adjacency of the adjacency
matrix matrix Relative Significance: Relative Significance: SignifSignif. times No. Nodes. times No. Nodes•• Relative Significance = 1, fair share of significanceRelative Significance = 1, fair share of significance
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Roadmap Roadmap
Identify a HierarchyIdentify a Hierarchy•• Defining the Importance of a nodeDefining the Importance of a node
Present topological propertiesPresent topological propertiesPresent the jellyfish model Present the jellyfish model Why is the jellyfish a good model?Why is the jellyfish a good model?ConclusionsConclusions
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Observation 1: Significance and Observation 1: Significance and Eccentricity Are CorrelatedEccentricity Are Correlated
Significant nodes have low eccentricitySignificant nodes have low eccentricityIntuitively, significant nodes are in the middle of the Intuitively, significant nodes are in the middle of the network network [Global Internet [Global Internet ‘‘01]01]
SignificanceSignificance
EccentricityEccentricity
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Observation 2: Many OneObservation 2: Many One--Degree Degree Nodes Connect to HighNodes Connect to High--Degree NodesDegree Nodes
OneOne--degree nodes are scattered everywheredegree nodes are scattered everywhereThe distribution of oneThe distribution of one--degree nodes follows a degree nodes follows a powerlawpowerlaw
Order of decreasingOrder of decreasingneighborsneighbors
Number of Number of 11--degreedegreeneighborsneighbors
The failure of The failure of FurballFurball modelmodel
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Observation 3: The Internet Premise:Observation 3: The Internet Premise:One Robust Connected NetworkOne Robust Connected Network
Robust to random, sensitive to focused failuresRobust to random, sensitive to focused failuresThe network tends to stay as one connected componentThe network tends to stay as one connected component
Size of Size of LargestLargestConnectedConnectedComponentComponent
0
1000
2000
3000
40000
332
664
996
1328
1660
1992
2324
2656
2988
I t er at i ons
Random
Highest Degree firstorderHighest Significancefirst order
#Deleted nodes#Deleted nodes
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Observation 4: The Number of Observation 4: The Number of Alternate Paths Between Two NodesAlternate Paths Between Two Nodes
All alternate paths go through the same directionAll alternate paths go through the same directionNo shortcuts or loopNo shortcuts or loop--aroundsarounds
Path Length
Number of pathsThe Failure of theDonut Model
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Roadmap Roadmap
Identify a HierarchyIdentify a Hierarchy•• Defining the Importance of a nodeDefining the Importance of a node
Present topological propertiesPresent topological propertiesPresent the jellyfish model Present the jellyfish model Why is the jellyfish a good model?Why is the jellyfish a good model?ConclusionsConclusions
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Defining a Hierarchy RecursivelyDefining a Hierarchy Recursively
Define the core:Define the core:•• Maximal clique of highest Maximal clique of highest
degree nodedegree node
Define the Layers:Define the Layers:•• All nodes adjacent to previous All nodes adjacent to previous
layerlayer
Define the Shells:Define the Shells:•• A layer without its oneA layer without its one--degree degree
nodesnodes
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The Internet Topology as a JellyfishThe Internet Topology as a Jellyfish
CoreCore: High: High--degree degree cliquecliqueShellShell: adjacent nodes of : adjacent nodes of previous shell, except previous shell, except 11--degree nodesdegree nodes11--degree nodesdegree nodes: shown : shown hanginghangingThe denser the 1The denser the 1--degree node population degree node population the longer the stemthe longer the stem
CoreShells 123
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The Hierarchy: The Model Respects The Hierarchy: The Model Respects the Node Importance the Node Importance
-6
-4
-2
0
2
4
6
8
Core Layer-1
Layer-2
Layer-3
Layer-4
Layer-5
Eff EccentricityLog Relative SignificanceLog Degree
The importance of The importance of nodes decreases as we nodes decreases as we move away from the move away from the corecoreThe effective The effective eccentricity decreases eccentricity decreases by one in each layerby one in each layer(see paper for details)(see paper for details)
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The Evolution of the JellyfishThe Evolution of the Jellyfish
The structure of the The structure of the jellyfish has not jellyfish has not changed much in changed much in 19971997--20002000Nodes become more Nodes become more connected:connected:Small increase in Small increase in shells and decrease shells and decrease in hanging nodesin hanging nodes
0
5
10
15
20
25
30
35
40
CoreHan
g-0She
ll1Han
g-1She
ll2Han
g-2She
ll3Han
g-3She
ll4Han
g-4
shell/hang
% o
f tot
al g
raph
8/ 11/ 1997 4/ 30/ 1998 8/ 1/ 1998 11/ 30/ 1998
4/ 30/ 1999 7/ 15/ 1999 10/ 10/ 1999 Jun-00
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The Diameter Remains ConstantThe Diameter Remains Constant
6 hops reach approximately 98% of the network!6 hops reach approximately 98% of the network!The jellyfish diameter remains the sameThe jellyfish diameter remains the same
PercentagePercentageof nodesof nodesreachedreached
TimeTime
HopsHops6655
44
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Theory Supports the Jellyfish!Theory Supports the Jellyfish!
A surprising theoretical result A surprising theoretical result [[ReittuReittu NorrosNorros 03]03]
•• A network with A network with powerlawpowerlaw degree degree --> jellyfish> jellyfish
Assume degree Assume degree powerlawpowerlaw and random and random connectionsconnections•• The network will have a clique of high degree nodesThe network will have a clique of high degree nodes•• The diameter of the network is O(log The diameter of the network is O(log logNlogN)!)!
In total In total aggrementaggrement with our observationswith our observations
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Why Is The Jellyfish a Good Model?Why Is The Jellyfish a Good Model?
ItIt’’s cute, in additions cute, in addition……
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The Jellyfish Captures Many The Jellyfish Captures Many PropertiesProperties
The network is compact:The network is compact:•• 99% of pairs of nodes are within 6 hops99% of pairs of nodes are within 6 hops
There exists a highly connected centerThere exists a highly connected center•• Clique of high degree nodesClique of high degree nodes
There exists a loose hierarchy:There exists a loose hierarchy:•• Nodes far from the center are less importantNodes far from the center are less important
OneOne--degree nodes are scattered everywheredegree nodes are scattered everywhereThe network has the tendency to be one The network has the tendency to be one large connected componentlarge connected component
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And It Looks Like A JellyfishAnd It Looks Like A Jellyfish……
Independent Independent ObservationObservationRouter Level Router Level TopologyTopologyProduced by CAIDAProduced by CAIDA
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Conclusions Conclusions
We model the Internet as a jellyfishWe model the Internet as a jellyfishThe jellyfish represents graphically several The jellyfish represents graphically several topological propertiestopological properties•• Network is compactNetwork is compact•• We can identify a centerWe can identify a center•• We can define a loose hierarchyWe can define a loose hierarchy•• The network tends to be one connected componentThe network tends to be one connected component
Theoretical results support our observationsTheoretical results support our observationshttp://http://www.cs.ucr.edu/~michaliswww.cs.ucr.edu/~michalis//
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My Other Research InterestsMy Other Research Interests
1.1. Characterize and model network behavior:Characterize and model network behavior:•• Poisson and Long Range Dependence [GI 02 Poisson and Long Range Dependence [GI 02 -- GlobecomGlobecom]]
2.2. Model and simulate the Internet topologyModel and simulate the Internet topology•• Identify structure and hierarchy [GI 01] [COMNET*]Identify structure and hierarchy [GI 01] [COMNET*]
3.3. Model and simulate BGPModel and simulate BGP•• Large scale simulations (10,000 nodes) [GI 02]Large scale simulations (10,000 nodes) [GI 02]
4.4. Wireless networksWireless networks•• Improving TCP over ad hoc networks [Improving TCP over ad hoc networks [GlobecomGlobecom 02]02]
5.5. Multicast: supporting scalability and Multicast: supporting scalability and QoSQoS (Cui (Cui GerlaGerla))•• Efficient management through overlay trees [Efficient management through overlay trees [GlobecomGlobecom 02]+02]+
6.6. A novel network layer: DART (A novel network layer: DART (PeerNetPeerNet) ) [IPTPS 03][IPTPS 03]
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Appendix:Appendix:Latest News on PowerLatest News on Power--lawslaws
The Internet topology can be described by The Internet topology can be described by powerpower--laws laws [Faloutsos x 3, SIGCOMM[Faloutsos x 3, SIGCOMM’’99]99]
The powerThe power--laws are here to staylaws are here to stay•• Appear consistently over five yearsAppear consistently over five years•• Even with newer more complete data [InfocomEven with newer more complete data [Infocom’’02]02]
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PowerlawPowerlaw: Degree Exponent D: Degree Exponent D
Degree distribution of nodes: CCDFDegree distribution of nodes: CCDFIt holds even for the more complete graph: 99%It holds even for the more complete graph: 99%
Newer More Complete AS graphNewer More Complete AS graphRouteViewsRouteViews -- NLANR DataNLANR Data
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Thank you!Thank you!
http://http://www.cs.ucr.edu/~michaliswww.cs.ucr.edu/~michalis//
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EigenvaluesEigenvalues of the Topologyof the Topology
Let Let A A be the adjacency matrix of graphbe the adjacency matrix of graphThe eigenvalue The eigenvalue λλ is real number s.t.is real number s.t.::•• A A vv = = λλ vv, , wherewhere vv some vectorsome vector
Eigenvalues are strongly related to topological propertiesEigenvalues are strongly related to topological propertiesMore details in Part BMore details in Part B
13
2 00 11 1111 00 0011 00 00
A =
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PowerPower--law: law: EigenEigen Exponent Exponent EE
Find the Find the eigenvalueseigenvalues of the adjacency matrixof the adjacency matrixEigenvaluesEigenvalues in decreasing order (first 100)in decreasing order (first 100)
E = -0.48
Exponent = slope
Eigenvalue
Rank of decreasing eigenvalue
May 2001
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Surprising Result!Surprising Result!
Exponent E is half of exponent DExponent E is half of exponent DTheorem: Given a graph with relatively large degrees Theorem: Given a graph with relatively large degrees ddii then with high probability:then with high probability:•• EigenvalueEigenvalue λλii == √√ ddii,, , where i rank of decreasing order, where i rank of decreasing order
Thus, if we compare the slope of the plot the Thus, if we compare the slope of the plot the eigenvalueseigenvalues and the degrees:and the degrees:•• log log λλii == 0.5 log 0.5 log ddii
[[FabrikantFabrikant, , KoutsoupiasKoutsoupias, , PapadimiitriouPapadimiitriou in STOCin STOC’’01]01][[MihailMihail Papadimitriou Random 02]Papadimitriou Random 02]
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Time Evolution of The Topology Time Evolution of The Topology
Powerlaws are here to stayPowerlaws are here to stayDegree distribution slope is invariantDegree distribution slope is invariantNetwork becomes denserNetwork becomes denserThe rich get richer phenomenonThe rich get richer phenomenon
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The Number of The Number of ASesASes in Timein Time
The number of AS doubled in two years The number of AS doubled in two years Growth seems to slow down!Growth seems to slow down!
3 K
13 K
1997 2002
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Degree Distribution Did Not Change!Degree Distribution Did Not Change!
Slope is practically constant for over 3 yearsSlope is practically constant for over 3 years
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The Topology Becomes Denser!The Topology Becomes Denser!
6 hops reach approximately 98% of the network!6 hops reach approximately 98% of the network!Denser: 6 hops reach more nodesDenser: 6 hops reach more nodes
Recall six Recall six degrees ofdegrees ofseparationseparation
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The Rich Get RicherThe Rich Get Richer
The increase of the degree versus the initial degreeThe increase of the degree versus the initial degreeNew connections prefer New connections prefer ““highly connected nodeshighly connected nodes””
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ThatThat’’s it!s it!
Thank you!Thank you!
http://http://www.cs.ucr.edu/~michaliswww.cs.ucr.edu/~michalis//
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I. PowerI. Power--law: rank exponent law: rank exponent RR
The plot is a line in logThe plot is a line in log--loglog scalescale
Exponent = slopeR = -0.74
R
degree
Rank: nodes in decreasing degree order
Dec’98
[Faloutsos, Faloutsos and Faloutsos SIGCOMM’99]
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I. Estimations Using With Rank Exponent I. Estimations Using With Rank Exponent RR
Lemma:Lemma:Given the nodes Given the nodes N, N, and an estimate for the and an estimate for the rank exponent rank exponent R, R, we predict the edges E:we predict the edges E:
NNR R ⋅−⋅
+=Ε + )11(
)1(21
1
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Some Current ResultsSome Current Results
Measuring the performance of realMeasuring the performance of real--time applicationstime applications•• E2e performance is asymmetric (by 10)E2e performance is asymmetric (by 10)
Estimating Long Range DependenceEstimating Long Range Dependence•• No definitive estimating method existsNo definitive estimating method exists•• SELFIS software tool for performance analysisSELFIS software tool for performance analysis
A study of BGP routing robustness A study of BGP routing robustness •• Persistence and prevalence of pathsPersistence and prevalence of paths•• Paths are fairly robust, but there is a lot of Paths are fairly robust, but there is a lot of ““noisenoise”” tootoo•• A data repository: 107Gb, 1 billion BGP pathsA data repository: 107Gb, 1 billion BGP paths
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Measuring RealMeasuring Real--time Performancetime Performance
““Can the Internet support Can the Internet support VoIPVoIP nownow??””We conduct globeWe conduct globe--wide experimentswide experiments
•• UCR, CMU, Japan, Australia, GreeceUCR, CMU, Japan, Australia, Greece
Experimental setExperimental set--upup•• Approx. 6 4Kbit/sec sending rateApprox. 6 4Kbit/sec sending rate•• Small packet sizes every 20, 30, 40, 50 Small packet sizes every 20, 30, 40, 50 msecmsec, 1 , 1
secsec
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How Many Distinct Paths Does an IP How Many Distinct Paths Does an IP Prefix Use?Prefix Use?
Almost 70% of the IP prefixes have Almost 70% of the IP prefixes have 22--10 distinct paths10 distinct paths30% of IP prefixes have only one path30% of IP prefixes have only one path
30%30%
70%70%
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For More InformationFor More Information
www.cs.ucr.edu/~michaliswww.cs.ucr.edu/~michalis//
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Routing Is PersistentRouting Is Persistent
CDF of the relative duration of CDF of the relative duration of the most persistent paththe most persistent path
70% of prefixes use 70% of prefixes use one path one path continuously for continuously for 50% of their time!50% of their time!
70%70%
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Measurements: The Death of the Measurements: The Death of the Symmetry Assumption Symmetry Assumption
OneOne--way delay:way delay:Forward can be 10 times higher than backward delayForward can be 10 times higher than backward delay
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Characterizing Network Behavior Characterizing Network Behavior with Long Range Dependence with Long Range Dependence
LRD captures the LRD captures the ““memorymemory”” of the behaviorof the behaviorIt is quantified by a single scalar numberIt is quantified by a single scalar numberLRD appears in many aspects of networksLRD appears in many aspects of networks•• Traffic load, arrival times, delays, packet lossTraffic load, arrival times, delays, packet loss
Open Question: what does it really tell us?Open Question: what does it really tell us?
PROBLEM:PROBLEM: We do not know how to calculate LRD!We do not know how to calculate LRD!•• Many estimators with conflicting estimatesMany estimators with conflicting estimates•• No systematic approachNo systematic approach
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The Intuition Behind LRDThe Intuition Behind LRD
White NoiseWhite Noise
Pink NoisePink Noise
Brownian NoiseBrownian Noise
Capturing the Capturing the ““dependencydependency”” of the signal to its of the signal to its previous valuesprevious values
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Idea: Reverse Engineering LRDIdea: Reverse Engineering LRDDevelop a library of behaviors to know dataDevelop a library of behaviors to know dataThree Series of Tests for the EstimatorsThree Series of Tests for the Estimators
1.1. Evaluating the accuracy of the estimatorsEvaluating the accuracy of the estimators•• Synthetic Fractional Gaussian Noise (FGN) Synthetic Fractional Gaussian Noise (FGN)
2.2. Deceiving the estimators with nonDeceiving the estimators with non--LRD data LRD data −− Periodicity, Noise, TrendPeriodicity, Noise, Trend
3.3. Applying the estimators in real data Applying the estimators in real data •• Characterizing delay and packet lossCharacterizing delay and packet loss
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BGP Routing AnalysisBGP Routing Analysis
Overarching Goal:Overarching Goal:•• Develop a realistic detailed model for large scale Develop a realistic detailed model for large scale
realistic simulationsrealistic simulations
Now: A study of BGP routing robustnessNow: A study of BGP routing robustness•• Persistence and prevalence of pathsPersistence and prevalence of paths•• Stability of advertisementsStability of advertisements
Next step: Next step: •• Study the customerStudy the customer--provider relationshipsprovider relationships
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Using Massive BGP Routing DataUsing Massive BGP Routing Data
We use data from NLANR for almost 3 yearsWe use data from NLANR for almost 3 years•• Late 1997 to early 2001Late 1997 to early 2001
Daily snapshots of BGP routing tablesDaily snapshots of BGP routing tablesCreated a database to facilitate path queriesCreated a database to facilitate path queries•• 107Gb of data, 1 billion BGP paths107Gb of data, 1 billion BGP paths
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Overview of Results for BGP RoutingOverview of Results for BGP Routing
Stable and persistent routing with some Stable and persistent routing with some ““noisenoise””44% prefixes are advertised for < 30 days44% prefixes are advertised for < 30 days50% prefixes have a dominant path 84% of time50% prefixes have a dominant path 84% of time35% of prefixes use one path continuously for 35% of prefixes use one path continuously for 90% of their time!90% of their time!Significant path multiplicity due to traffic Significant path multiplicity due to traffic enginengin..
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Graph Reduction ToolsGraph Reduction Tools
Reduce: large real graph to small realistic graphReduce: large real graph to small realistic graph•• Achieve 70% reduction Achieve 70% reduction
Satisfy degree distribution, but increases diameterSatisfy degree distribution, but increases diameter
Reduce
Large
Small
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The Jellyfish Captures The Jellyfish Captures ““DirectionDirection””of Connectivityof Connectivity
Most edges are Most edges are between layers between layers 80% 80% Less edges are Less edges are within a layer within a layer 20%20%
05
1015202530354045
Layer
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4/ 30/ 1999 7/ 15/ 1999 10/ 10/ 1999 Jun-00
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The Model Respects the Node The Model Respects the Node ImportanceImportance
-3
-2
-1
0
1
2
3
4
5
6
7
Core Shell-1 Shell-2 Shell-3 Shell-4
Effective EccentricityLog Relative SignificanceLog Degree
The importance of each The importance of each layer decreases as we layer decreases as we move away from the move away from the corecore
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Intuitive Models Are UsefulIntuitive Models Are Useful
Cons:Cons:•• Danger of oversimplificationDanger of oversimplification
Pros:Pros:•• MemorableMemorable•• VisualizableVisualizable•• Maximizing information/effort ratioMaximizing information/effort ratio
They can be very useful when exploring They can be very useful when exploring unknown territoryunknown territory•• Even disproving a wrong model is progress!Even disproving a wrong model is progress!